The Cauchy-Goursat theorem states that within certain domains the integral of an analytic function over a simple closed contour is zero. An extension of this theorem allows us to replace integrals over certain complicated contours with integrals over contours that are easy to evaluate. In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat ), is an important statement about line integrals for holomorphic functions in the complex plane.

Cauchy’s integral theorem An easy consequence of Theorem 7.3. is the following, familiarly known as Cauchy’s integral theorem. Theorem 7.4.If Dis a simply connected domain, f 2A(D) and is any loop in D;then Z f(z)dz= 0: Proof: The proof follows immediately from the fact that each closed curve in Dcan be shrunk to a point. Q.E.D. From Wikipedia, the free encyclopedia. In mathematics, Cauchy's integral formula, named after Augustin Louis Cauchy, is a central statement in complex analysis.It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk. Math 311 - Spring 2014 Solutions to Assignment # 8 Completion Date: Friday May 30, 2014 Question 1. [p 149, #2] By nding an antiderivative, evaluate each of these integrals, where the path is any contour between the